DESCRIPTION: Clinical trials are frequently constructed with surrogate endpoints, for practical or cost considerations. Often such trials are used to make implicit inferences about the effect of treatment on a more critical endpoint, such as survival. This translation is often made by medical investigators if the surrogate is known to be correlated with the true endpoint, but without reference to the strength of this association. The general purposes of this proposal are to examine,in a quantitative way, the extent to which such inferences are justifiable, and to develop and evaluate new statistical methods that account for the dependencies in a more complete way. Specifically, we will examine the mathematical relationships between the parameters characterizing the associations between each of the variables, focusing on odds ratios for binary data and proportional hazards models for survival-type data. Using these results we will develop a conceptual strategy for interpreting the results of trials with surrogate endpoints. We will develop a method for optimizing the sample size for pilot screening trials employing surrogate endpoints, useful in chemoprevention research. We will study the properties of estimated likelihood methods which may have utility in conventional trials where the surrogate endpoints are used to augment the limited information on the true end-point. Finally the applicants will apply the methods to numerous relevant datasets available at their Center.